New Methodology for Unbiased Ground-Motion Intensity Conversion Equations

Abstract

ABSTRACT Ground-motion intensity conversion equations (GMICEs) allow for conversions between ground-motion amplitude and shaking intensity. The current methods used to develop GMICEs model the dependence of the intensity on the peak ground-motion (PGM) parameter. For some models, there is a second step that models the magnitude and distance dependence of the residuals from the initial regression. We show that this approach for developing GMICEs works well for estimating the intensity from median ground motions, but for ground-motion values away from the medians, the intensities estimated by the GMICE can have large bias, with overprediction for positive PGM residuals and underprediction for negative PGM residuals. The bias is due to an implicit assumption in the current approach that there is a direct causal relation between intensity and the ground-motion parameter and that the residuals of the intensity and ground-motion parameter are fully correlated. We present two alternative methodologies for developing GMICEs that do not suffer from this bias. The first method includes the magnitude and distance scaling of the GMICE in the initial regression for the scaling with the PGM. The second method excludes the magnitude and distance terms but includes the number of standard deviations of the PGM (ϵ) as an additional parameter in the GMICE. Using a synthetic data set of intensity and peak ground acceleration values, we show that the GMICE developed using the proposed method leads to more accurate estimates of the intensity than current methods. We also discuss implications of using GMICEs based on the proposed methods for the evaluation of probabilistic hazard maps and as input to ShakeAlert estimates.